Quick Introduction to Phase Margin
Excess phase shift in an operational amplifier can cause oscillation in the user’s application
Defining Phase Margin
• Applies to feedback around an amplifier with negative gain at low frequency
• If |Gain| > 1 and phase shift > 180 degrees, the circuit oscillates • If phase is too close to 180 degrees gives overshoot to step input
• Phase margin for the amplifier is how many degrees of phase shift could be added too the loop gain by the feedback block K(s) before oscillation would start Open loop gain is defined as: GOL  A s K  s
Usually phase is a monotonic function so the phase margin is 180 – Phase(A(s)) at frequency for which |A(s)| = 1X (0 dB)
180
140
LF353 Open Loop Gain
120
160
Gain in dB
Unity Gain Point (2.8 MHz)
100
140
Phase shift in degrees
80
Gain (dB)
60
100
40
80
20
60
0
Phase margin for the LF353 – 64 deg.
‐20
40
20
‐40
‐60
10
100
1,000
10,000
100,000
Frequency (Hertz)
1,000,000
10,000,000
0
100,000,000
Phase Shift (degrees)
120
Schematic of Phase Shift Oscillator
Open Loop Gain and Phase of Oscillator Circuit
100
140
80
100
Phase margin is minus 40 degrees
60
Gain (dB)
180
60
20
40
Open Loop Gain in dB
Zero Phase Frequency (450 KHz)
20
‐20
Phase Shift in Degrees
‐60
0
‐20
‐100
‐40
‐140
‐60
‐180
10,000,000
10
100
1,000
10,000
Frequency (Hertz)
100,000
1,000,000
Phase (degrees)
120
V(vout)
20
18
16
Output Signal (volts)
14
12
10
8
6
4
2
0
0.00E+00
1.00E‐05
2.00E‐05
3.00E‐05
Time (seconds)
4.00E‐05
5.00E‐05
Common Source Stage with Miller Compensation
• Complete Circuit
• Small Signal Model
– Omits CGS and CGD
Transfer Function with RM = 0
Zero – Bad for phase!!! H (s) 
 g m rO 1  sCM / g m 
s CO roCM ri  s  1  g m rO  CM ri  CO rO  CM rO   1
2
Second pole Miller effect
Dominant pole
Transfer Function with RM in Place
Zero term bad for phase
H (s) 
 g m rO 1  sCM / g m  sCM RM 
Zero – New term good for phase
Make RM > 1/gm
s CO roCM  ri  RM   s  1  g m rO  CM ri  CO rO  CM rO  CM RM   1
2